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From: <GSLevy.domain.name.hidden>

Date: Tue, 22 Jun 1999 03:24:19 EDT

Jaques Mallah's role is important in that he forces us to confront important

issues. However, he could more effectively communicate by "polishing" his

style. Enough said of that. Wei Dai has summarized the issue very well.

In a message dated 99-06-19 18:29:26 EDT, Wei Dai writes:

<<

I think the main point of disagreement between the two camps now is

relative SSSA versus absolute SSSA (Marchal's terms). Can we all agree

that given the absolute SSSA, there is no justification for QS? >>

My understanding of the "Strong" Self Sampling Assumption is shaky, but I

think I agree with the above statement. I would find it clearer if it could

be rephrased as follows: If the number of branching in the MW is absolute

then there is no justification for QS.

This is the crux of the matter.

Jaques Mallah's position is summarized in his words:

<< Your total measure would be reduced, so there would be less

observers with that name in the ensemble, and the total number of

observers would be less. >>

Clearly Jacques views the number of branches in the MW as absolute and

limited. If you do QS and trim a few branches you just end up with less

branches. The more stringent the QS conditions (winning a $1million or a

$1billion or having Elvis Presley come back to life) the smaller the number

of branches you end up in. And if you make the conditions too stringent you

may end up with nothing. No more of you.

If however, the number of branches does not change no matter where you are in

the MW -- according to a kind of a super Cosmological Principle -- then no

matter how many times you commit QS, you still have the same number of

branches left. This, I think, is the "relative" SSSA that Wei Dai and Marchal

are talking about. Adding branches or subtracting branches has no impact on

the probability of your future existence. And it is precisely in the

discussion of probability in this environment that some of the hottest

discussions with Jacques have taken place.

So which is it? absolute and limited number of branches or relative and

unlimited?

I think that the discussion hinges around the size of the MW. If the size is

finite, then there is no question, in my mind that Jacques is right. The

number of branches is finite and QS just trims the MW tree (or network). If

however, the MW is infinite, then the answer is more difficult.

Imagine the MW to be infinite aleph1 just like the number of points on a

line. In this environment the super Cosmological Principle I mentioned above

applies: no matter how many times you cut that line, the number of points on

any segment is still aleph1. This number is like the speed of light: a

physical constant of that world: aleph1, independent of the observer's

position -- or line segment.

So one condition for justifying QS is having an infinite MW. -- I am not sure

what is the lowest of Cantor's infinities would correspond to a sufficient

condition.

A second condition is that the number of branches "cut" by QS should be

infinitely smaller than the infinity of the MW. (ie Aleph QS < Aleph MW)

I would like to add that on purely philosopical grounds I can only conceive

of an absolute infinitely large MW, larger than all of Cantor's infinities --

because any other size would have to be arbitrary and therefore have a reason

to be so. And this limited MW would end up being just one instance of many

other MW in a larger MMW.

So which is it? Is the MW finite or infinite? Is QS justified?

This said, I think that NOTHING justifies QS. My position however is ethical.

As the idea of the MW matured in my mind, I have become convinced that while

the MW is absolutely infinite, it is possible to avoid the nihilist

philosophy of Friedrich Nietzsche and evolve an ethic of the many worlds. In

fact the JUSTIFICATION FOR QS COULD BE TURNED ON ITS HEAD as I have pointed

out in my last post. Beautifully said in the 23rd psalm: "The Lord is my

shepherd, I shall not want...the shadow of the valley of death (the MW)... I

shall fear no evil... .my cup runneth over" The knowledge that we are

immortal and that all stings and arrows are temporary can give us a new

perspective on the world.

George Levy

Received on Tue Jun 22 1999 - 00:28:47 PDT

Date: Tue, 22 Jun 1999 03:24:19 EDT

Jaques Mallah's role is important in that he forces us to confront important

issues. However, he could more effectively communicate by "polishing" his

style. Enough said of that. Wei Dai has summarized the issue very well.

In a message dated 99-06-19 18:29:26 EDT, Wei Dai writes:

<<

I think the main point of disagreement between the two camps now is

relative SSSA versus absolute SSSA (Marchal's terms). Can we all agree

that given the absolute SSSA, there is no justification for QS? >>

My understanding of the "Strong" Self Sampling Assumption is shaky, but I

think I agree with the above statement. I would find it clearer if it could

be rephrased as follows: If the number of branching in the MW is absolute

then there is no justification for QS.

This is the crux of the matter.

Jaques Mallah's position is summarized in his words:

<< Your total measure would be reduced, so there would be less

observers with that name in the ensemble, and the total number of

observers would be less. >>

Clearly Jacques views the number of branches in the MW as absolute and

limited. If you do QS and trim a few branches you just end up with less

branches. The more stringent the QS conditions (winning a $1million or a

$1billion or having Elvis Presley come back to life) the smaller the number

of branches you end up in. And if you make the conditions too stringent you

may end up with nothing. No more of you.

If however, the number of branches does not change no matter where you are in

the MW -- according to a kind of a super Cosmological Principle -- then no

matter how many times you commit QS, you still have the same number of

branches left. This, I think, is the "relative" SSSA that Wei Dai and Marchal

are talking about. Adding branches or subtracting branches has no impact on

the probability of your future existence. And it is precisely in the

discussion of probability in this environment that some of the hottest

discussions with Jacques have taken place.

So which is it? absolute and limited number of branches or relative and

unlimited?

I think that the discussion hinges around the size of the MW. If the size is

finite, then there is no question, in my mind that Jacques is right. The

number of branches is finite and QS just trims the MW tree (or network). If

however, the MW is infinite, then the answer is more difficult.

Imagine the MW to be infinite aleph1 just like the number of points on a

line. In this environment the super Cosmological Principle I mentioned above

applies: no matter how many times you cut that line, the number of points on

any segment is still aleph1. This number is like the speed of light: a

physical constant of that world: aleph1, independent of the observer's

position -- or line segment.

So one condition for justifying QS is having an infinite MW. -- I am not sure

what is the lowest of Cantor's infinities would correspond to a sufficient

condition.

A second condition is that the number of branches "cut" by QS should be

infinitely smaller than the infinity of the MW. (ie Aleph QS < Aleph MW)

I would like to add that on purely philosopical grounds I can only conceive

of an absolute infinitely large MW, larger than all of Cantor's infinities --

because any other size would have to be arbitrary and therefore have a reason

to be so. And this limited MW would end up being just one instance of many

other MW in a larger MMW.

So which is it? Is the MW finite or infinite? Is QS justified?

This said, I think that NOTHING justifies QS. My position however is ethical.

As the idea of the MW matured in my mind, I have become convinced that while

the MW is absolutely infinite, it is possible to avoid the nihilist

philosophy of Friedrich Nietzsche and evolve an ethic of the many worlds. In

fact the JUSTIFICATION FOR QS COULD BE TURNED ON ITS HEAD as I have pointed

out in my last post. Beautifully said in the 23rd psalm: "The Lord is my

shepherd, I shall not want...the shadow of the valley of death (the MW)... I

shall fear no evil... .my cup runneth over" The knowledge that we are

immortal and that all stings and arrows are temporary can give us a new

perspective on the world.

George Levy

Received on Tue Jun 22 1999 - 00:28:47 PDT

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